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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Uniqueness of positive radial solutions of $ \Delta u+f(u)=0$ in $ {\bf R}\sp n$. II


Author: Kevin McLeod
Journal: Trans. Amer. Math. Soc. 339 (1993), 495-505
MSC: Primary 35J60; Secondary 34B15, 35B05
MathSciNet review: 1201323
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Abstract: We prove a uniqueness result for the positive solution of $ \Delta u + f(u) = 0$ in $ {\mathbb{R}^n}$ which goes to 0 at $ \infty $. The result applies to a wide class of nonlinear functions $ f$, including the important model case $ f(u) = - u + {u^p}$ , $ 1 < p < (n + 2)/(n - 2)$. The result is proved by reducing to an initial-boundary problem for the $ {\text{ODE}}\;u'' + (n - 1)/r + f(u) = 0$ and using a shooting method.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1201323-X
PII: S 0002-9947(1993)1201323-X
Article copyright: © Copyright 1993 American Mathematical Society